Self-Assembly of Colloidal Nanocrystals into Ordered Superstructures
Recent studies have demonstrated enormous structural diversity in multicomponent nanoparticle assemblies, leading to a multitude of complex phases combining semiconducting, metallic, and magnetic nanocrystals into long-range ordered binary nanocrystal superlattices (BNSLs) [3D Magnetic BNSLs, Structural Diversity of BNSLs]. Over the last few years we have extensively studied BNSL formation [Structural Defects in BSNLs, Energetic & Entropic Contributions to BNSL Self-Assembly, Size-Dependent Multiple Twinning in NC Superlattices], focusing on several aspects described below.
At present, there is no clear understanding of the processes that
govern the assembly of colloidal nanoparticles into complex
multicomponent structures. On the other hand, the physics of sphere packing is rather well understood, with numerous theoretical and experimental studies outlining the effects of entropy [Entropy-Driven Formation of a Binary Superlattice, Binary Superlattice Formation in Hard-Sphere Colloids, Substitutionally-Ordered Solutions of Hard Spheres], pair potentials [Ionic Colloidal Crystals, Nanoscale Forces in Self-Assembly, Interparticle & External Forces in NC Assembly, Crystal Structures of Oppositely-Charged Colloids, 3D Binary Superlattices of Oppositely-Charged Colloids] and polydispersity [Suppression of Nucleation in Polydisperse Colloids] on the nucleation and growth of ordered phases.
To apply this framework to colloidal nanocrystals, we need quantitative estimates for the terms contributing to the free energy (F = U - TS) associated with the disorder-to-order transition in nanocrystal assemblies. We studied the hierarchy of the energy scales acting during self-assembly of nanocrystals and have shown that the structural diversity of BNSLs is a result of the cooperative effect of the entropy-driven crystallization and the interparticle interactions. Both ΔU and TΔS terms associated with the superlattice formation have the same order of magnitude [LEGO Materials].
Moreover, temperature can be used as the weighting factor for the internal energy (U) and entropy (S) contributions and allows tailoring the relative weights of the interparticle interactions and free-volume entropy during the formation of nanocrystal superlattices. An amazing example of this effect is shown in Figure 2. Free-energy calculations predict no stable binary phases for a mixture of hard spheres with the size ratio γ=0.74 [Stability of LS & LS2 Crystal Structures in Binary Charged Mixtures], whereas PbSe and Pd nanocrystals with same γ formed six (!) different BNSL phases at different temperatures [Energetic & Entropic Contributions to BNSL Self-Assembly]. From the practical side, temperature provides a convenient tool for directing self-assembly of nanocrystals toward desired BNSL structures.
BNSL Structural Complexity and Self-Assembly
of Quasicrystalline Superlattices
We studied the formation of amazingly complex binary structures from spherical iron oxide and gold nanoparticles (Figure 3) and revealed their topological connections to the Archimedean tilings, defined as the regular patterns of polygonal tessellation of a plane by regular polygons, where only one type of vertex is permitted [Quasicrystalline Order in Self-Assembled BNSLs]. The Archimedian tilings are known as the unique pseudomorphic phases that can combine both periodic and aperiodic structural elements [A Tale of Two Tilings, Archimedean-Like Tiling on Quasicrystal Surfaces].
Careful exploration of BNSL phase diagrams allowed us to extend the borders of self-assembly to quasicrystalline nanoparticle superlattices. Quasicrystals generate sharp diffraction peaks while lacking any translational symmetry and often showing symmetry operations forbidden in classical crystallography. We demonstrated that different mixtures of colloidal nanocrystals can self-assemble into quasicrystalline structures with “forbidden” twelvefold rotational symmetry (Figure 4).
Our work introduced a new class of materials with quasicrystalline order. The compositional flexibility of qualicrystalline BNSLs indicated that the quasicrystalline ordering could be a common phenomenon in nanocrystal solids. Our work also showed how the cooperative effect of the free-volume entropy and configurational entropy can lead to the formation of quasicrystalline phases from spherical particles, even in the absence of any directional forces. Nanoparticle quasicrystals helped solving a longstanding problem about the possibility of a smooth transition between topologically different quasicrystalline and crystalline phases. We observed that such transition requires a thin “wetting layer” of (33.42) Archimedean tiling which matched both phases with a low concentration of interfacial defects.